A class is a "type" where objects can be instantiated from.
Classes in most programming languages are properties (variables) and functions grouped together. Think of them like objects in the real world. A book class, for instance, might have properties for its name, author, and number of pages, and functions such as turning a page. You can have multiple things with the same class (instances) existing at the same time, and with different properties, eg book A with 30 pages and book B with 50.
If you're feeling brave, have a look at the Wikipedia page on Object-oriented programming.